Mahombekombe anonzi vatakuri vepamusoro, vane pamusoro wepakati usina kuenzana asi wakabudikira zvinoonekwa. Maitiro avo ekumira anosiyana zvikuru neaya eplati. Kana aine chimiro chinokodzera, kushushikana kwawo kunenge kwakaderera zvikuru, kusimba kwawo kwakakura zvichienderana, uye kuverenga kwawo kazhinji kuri nyore.
Kushushikana kwegoko rega rega kunogona kupatsanurwa kuita zvikamu zviviri: kushushikana kwemembrane uye kukotama. Kushushikana kwemembrane, sezvakangoita kushushikana kweplate rakaremerwa mumwero waro, kunogona kuratidzwa kuburikidza nemasimba ekucheka ari mundege yetangenti - aya semuenzaniso muchikamu x=const. simba rakajairika _Nx=_σx*t uye simba rekutsvedza _Nxy=_τxy*t, apo t iri ukobvu hwegoko. Kushushikana kunokonzerwa nekukotama kwakafanana nekwemaplate uye kunogona kuratidzwa nemameneti ekukotama Mx, mameneti etorsion Mxy uye masimba ekutsvedza Qx.
Zvinhu zvakakosha zvemagoko zvinobva pachokwadi chekuti kazhinji kushushikana kunokonzerwa nekukotama hakunei nehukuru kana kukosha kwekushushikana kwemembrane, saka kazhinji kunogona kufuratirwa zvachose. Muchiitiko ichocho, kushushikana kwese kunopatsanurwa zvakaenzana pakukora kwegoko uye kunoshanda tangentially panzvimbo yepakati. Kuverenga kunovakirwa pane izvi zvimiro kunopinda muchimiro chedzidziso yemembrane yemagoko.
Dzidziso yemembrane yegobvu dzine symmetry yekutenderera pasi pemutoro une symmetry yekutenderera
Mafomu akajairika
Pamitsetse yecoordinate panotorwa meridians nemadenderedzwa akafanana pamusoro pepakati pehombodo, saka ma coordinate ndiwo: azimuth ϑ (“longitudo yegirafu”) uye kukombama φ kwe tangent kumeridian kunoenda kune plane yakatwasuka kuenda kuaxis yesymmetry (muf. 1a). Naizvozvo masimba ekucheka ndeaya: simba renormal Nφ munzira yemeridian uye simba renormal Nϑ muringi (muf. 1b). Masimba ekucheka Nφϑ haabudi pakumanikidzwa kunoenderana nesymmetry yekutenderera. Mutoro pachikamu chimwe chepamusoro unoratidzwa seizvi (muf. 1b): Y iri tangent kumeridian, yakanaka munzira inokwira φ, Z yakatarisana nehombodo, yakanaka yakananga kuaxis yesymmetry.
Muf. 1
Fig. 2
Ngatifungidzire kuti radius yekukombama kwemeridian ndeye r1. Iri ibasa rekona φ saka nechiyero _r1=r1(_φ) chimiro chaimeridian chinotsanangurwa. Izvi zvinogona kutorwa sechiyero chemeridian uye zvinoti, semuenzaniso.
kudenderedzwa r1=a=const.
kune parabolu r1=a/cos3__φ
kune elipse r1=a2b2(a2sin2__φ+b2cos2__φ)-3/2
Kuti kuverengerwe simba rakajairika N__φ munzira yemeridiani, zvinofanira kuiswa mamiriro ekuenzana kwechikamu chechipoloro chinovepo pamusoro pedenderedzwa rakaenzana φ (muf. 2). Mhedzisiro R yemitoro Y ne Z inobata chikamu ichi yakatwasuka, maererano nekuenzanirana. Hukuru hwayo hunowanikwa nekuunganidza pamusoro pepamusoro pechipoloro kubva φ’=0 kusvika φ’=φ. Nzvimbo yechinhu chechipoloro ndeye dF=r1d__φ’*rd__ϑ, saka chikamu chakatwasuka chemutoro (Ysin__φ’+Zcos__φ’)dF. Kune chikamu chese chemhete chechipoloro chiri pakati pemadenderedzwa φ’ ne φ’+dφ’ mhedzisiro yemutoro wekunze ndeiyi:
dR=2__πr (Ysin__φ’+Zcos__φ’) r1d__φ’,
kubva ipapo, nekubatanidza maererano ne φ’ yechikamu chehombodo chiri pamusoro pedenderedzwa rinofambirana φ’=φ tinowana:
Eq. 1
Mutoro uyu unotorwa nemasimba akajairika ari munzira yemeridiani, anoita kutenderedza denderedzwa rinoonekwa; chikamu chakatwasuka chekuungana kwemasimba aya ndi 2__πr * N__φ sin__φ, saka nekufananidza kubva pano tinowana simba rakajairika rinodiwa
Chikamu 2
Kana goko riri pamusoro rachekwa richitevedza denderedzwa φ=φ0 (semuenzaniso, kuvhura kwechiedza mudome), muganhu wepasi weintegral ndiwo, sezvinongoita, φ0, kwete zero. Kana pachipendero chegoko chakaita nenzira iyi pakashandawo mutoro R0, iwowo unofanira kuwedzerwa kune chibereko R (muf. 3).
Fig. 3
Kuti kuoneswe simba rakajairika N__ϑ zvinodikanwa kumisa mamiriro ekuenzanisa kwechinhu chegoko chakatarisana neplane yetangential (fig. 4). Chiyero chemutoro wekunze munzira iyi chinoita Z r1 d__φ r d__ϑ. Masimba N__φ*r d__ϑ ari muplane yemaridiyeni anoumba kona diki d__φ pakati pawo, saka chiyero chawo munzira yechinjiso chegoko ndi N__φ r d__ϑ*dφ. Saizvozvowo, masimba Nϑ r1 dφ ari muplane yedenderedzwa rakachinjika uye anoumba kona dϑ pakati pawo ane chiyero Nϑ r1 dφ*dϑ icho chinobatwawo muplane yedenderedzwa rakachinjika uye nokudaro chinoumba kona 0,5_π-φ_ ne normal yegoko, saka muchimiro chekuenzanisa panopinda chikamu chavo chete Nϑ r1 dφ dϑ*sinφ. Saka mamiriro ekuenzanisa anoti
kana, kana zvikagoverwa ne r r1 dϑ dφ:
Poshi.3
Pano ne r2=r/sinφ panotsaurwa hafu yeredhiyasi yechipiri huru yecurvature yegoko.
Muf. 4
Dhongi rematenderedzwa
Kana chimiro chemeridiani chapihwa nenzira yechiverengero r1=r1(φ) uye kana pamitoro Y(φ) ne Z(φ) dzapihwa matauriro echiverengero, masimba ekuchinjisa mugobvu anogona kugara achiwanikwa nekubatanidza muchimiro chakavharwa kana nenhamba, tichishandisa Simpson-o mutemo. Padhomu rakatenderera rine dhayamita a, pazasi pano kupiwa masimba ekuchinjisa kune dzimwe nyaya dzemutoro:
Mufanidzo wekupedzisira, unopa pak φ=0 masimba ekuchera asingaperi akakura, unoshanda chete pane chinhambwe chakati kubva panzvimbo inokurirwa nesimba. Munzvimbo iri pedyo chaizvo nepo simba richishanda, kunyangwe richigoverwa pamusoro pedenderedzwa rine dhayamita yakazara asi diki, mutoro unonyanya kufambiswa nekukotama.
Maitiro emacarcas akavhurika kumusoro anogona kubviswa kubva kune apfuura, kana pakuremerwa kwechokwadi pakawedzerwa mutoro wekunyepedzera P pamuromo, ukuru hwacho hunotemerwa kudaro kana simba rose rakajairika rakananga meridian rinoshanda pamucheto wepamusoro pecarcas φ=φ0 riri Nφ=0, kana kuti rakaenzana nehumwe huwandu hunotemerwa nemasimba ekunze anogamuchirwa pano necarcas.
Chipoloro chekoni
Muf. 5
Pamagoko ekooni, kurerekera kwemeridiani φ hakugoni kushandiswa sechinhu chinomiririra nzvimbo, nokuti kune kukosha kumwe chete panzvimbo dzose. Pane izvozvo, panoshandiswa kureba s kubva pamusoro wedome, kuyerwa pamwe neanogadzira (muf. 5). Simba rakajairwa munzira yemeridiani rinomakwa sa Ns. Mafomu anodiwa anogona kuwanikwa kubva kune akapihwa pasi pe1 kana muganho uchinge waitwa. Kubva paequation (2) zvinowanikwa nenzira iyoyo
uye kubva muequation (3)
Nϑ = -r2 Z = -Z s ctga.
Panyaya huru dzekuremerwa, zvinotevera mafomura zvinoshanda:
Nzira yegirafu yechimiro chipi nechipi chemeridiani
Fig. 6
Kana curve ye meridiana isina kupihwa nechirevo chekuongorora, asi, semuenzaniso, nechimiro chegirafu, kutsanangura radius yekukotama kunonetsa zvikuru uye hakuna kunyatsorurama. Muchiitiko ichocho zviri nani kushandisa nzira yegirafu (sl. 6).
Ganda rinopatsanurwa nemapani mazhinji φ=const., huremu hwezoni dzemaringi Δ_R_ dziri pakati pemapani hunoverengwa, uye zvakanaka kuti dzigovanwe pakarepo ne 2_π_. Aya masimba ΔR/2π anoiswa mupurani remasimba (muf. 6b). Kana zvino, semuenzaniso, kuburikidza nenzvimbo yekupatsanura 7 kukweverwa mutsetse wakaenzana netangenti kumeridiyani panzvimbo yemeridiyani 7, mutsetse wakatwasuka uri pamusoro pepurani remasimba uchaiyambuka pairi kureba R1/2π sinφ7 kubva kwarinobva, maererano neequation (2) nekukamura neiyo r yakakodzera, simba rakajairika rinowanikwa munzira yemeridiyani.
Pakutsanangura masimba mumaringi, inoshandiswa mutemo wekuenzana kwemasimba akatwasuka pane chimwe chikamu chegobvu. Kana pane chete mitoro yakatwasuka, mutemo uyu unoti (sl. 4):
Kana pano dφ ikatsiviwa nemusiyano wekupedzisira Δφ, unoenderana nekupatsanurwa kwakatorwa kwehombodo, uye kana panzvimbo ye r1 dφ kukaiswa kureba Δs kwechinhu chemeridiani, pano panowanikwa
Mubraketi kurutivi rwerudyi mune chikamu chinobva pamutsetse wakachinjika muhurongwa hwemasimba. Saka rutivi rwose rwerudyi runomirira zvikamu zviri pakati pemapoinzi ekugovanisa pamutsetse uyu. Kuti tikwanise kuzviverenga nemazvo zvakakwana, hurongwa hwemasimba hunofanira kudhirowewa nokungwarira uye nechikero chikuru chakakwana.
Maringi akatambanudzwa uye akatsikirirwa
Goko rega rega rine symmetry yekutenderera rinogumirwa nedenderedzwa rimwe kana maviri akachinjika (muf. 7). Pamicheto iyi rinogona, muchimiro chayo, kugamuchira chete mitoro yakadaro nemaitiro ezvinotsigira ane gwara retangenti kune meridian. Kana masimba ekunze aine rimwe gwara, semuenzaniso mutoro P unobva muchikamu chepamusoro chechimiro kana kuita S kwepasi retangi rinoratidzwa pamuf. 97, masimba aya anofanira, sezvinoratidzwa pamufananidzo, kupatsanurwa kuita zvikamu zviri mugwara redenderedzwa rakachinjika uye tangenti kune meridian. Chikamu P/sinφ0 kana S/sinφu chakaenzana nesimba rakajairika mugwara remeridian Nφ rinoshanda ipapo, ukuwo pakugamuchira simba rakachinjika Pctgφ0 kana Sctgφu panodiwa mhete inogamuchira kudhonza, kana kudzvanya, uye umo mutoro weradial uyu unokonzera simba rakajairika + P r0 ctgφ0, kana -S ru ctgφu. Mhete dzakadaro, kunze kwemipendero yegoko, dzinofanira kuiswa zvakare panzvimbo dzose apo meridian curve ine kupeteka. Nguva dzose dzinokonzera kukanganisika kwemamiriro ekushushikana kwenhanho.
Muf. 7
Kushushikana kunokonzerwa nekukotama mumagoko anotenderera ane symmetry
Mafomu edzidziso yediaphragm haana huwandu hwakakwana hwemakonstanto ekubatanidza kuti miganho yose chaiyo inoenderana nebasa rakapiwa igone kuzadzikiswa. Kunyanya pamagoko ane symmetry yekutenderera, hazviiti kuti nekusarudza zvakanaka makonstanto ekubatanidza, kuwedzera εϑ = Nϑ/Et munzira yeringi parutivi rwegoko kuenzane nekuwedzera kunoenderana kwechimwe chikamu chechimiro chakabatana naro panzvimbo iyoyo zvakasimba. Izvi zvinoshandawo kumagoko ayo, parutivi rwerimwe denderedzwa rakatwasuka, ukobvu hwemeridiani, ukobvu hwegoko kana mutoro paunit yenzvimbo zvinoshanduka pakarepo. Kana goko risina kusimbiswa neringi parutivi rwaro, asi panzvimbo iyi richiremerwa nemasimba ane chikamu munzira yakatwasuka pagoko (semuenzaniso mutoro P pamuf. 7 kana zvichifungidzirwa kuti ring yabviswa), harikwanisi kugamuchira mitoro yakadaro kuburikidza chete nemasimba emembrane. Mumamiriro akadaro simba rekucheka nemamoment ekukotama (muf. 8) zvinotamba basa guru mukugoverwa kwemasimba mugoko, izvo zvinofanira kutorwa mukufungisisa pakuverenga kwechimiro.
Muf. 8
Kuverenga chaiko kwekabhomba pakukotama, kunze kwechiitiko chakareruka zvikuru chepamusoro chakanangana nekabhomba recylindrical, ibasa rakaoma kwazvo. Kune makabhomba ane madziro matete, rinogona kuvakwa dzidziso iri nyore uye inobatsira zvikuru inofungidzirwa, inotsamira pachokwadi chinozivikanwa kubva mudzidziso yakasimba, kuti kusakara kunokonzerwa nekukotama kunogumira munzvimbo yakatetepa pedyo nemucheto uye kunoderera nokukurumidza sezvo chinhambwe kubva kumucheto chichiwedzera. Izvi zvinoita kuti nhamba huru yemashoko muequation chaiyo yakasiyanisa isaregerwe, zvobva zvaita kuti iwane chimiro chakareruka.
Kana mukati memuganhu unokosha κ katsiviwa neavhareji yawo, uye izvi zvinowanzoita kuti zviitike, mhinduro yeequation ndeye
Jedn. 4 na 5
panova a1, b1, a2, b2 ari maconstant ekubatanidza. Sezvo mhinduro ichinakidza chete pedyo nemuganhu φ=φ0, zvakanaka kutora chinhambwe chekona ω=φ0-φ kana ω=φ-φ0 kubva pamuganhu uyu semurongero, uye pakushandura mhinduro iri pamusoro tinowana chirevo chechipiri chataurwa. Pano panongoonekwa maconstant maviri ekubatanidza A, B kana C, ψ, nokuti chikamu chechipiri chemhinduro chine chinhu eκω, uye nokudaro, kana ω ichiwedzera, hachidzikiri, chinogona kusiiwa kubva mukufungisisa.
Zvichienderana neequation 5 zvinowanikwa zvinotevera zvimiro zvesimba dzinocheka uye kutenderera κ kwetangiendi remeridian:
Manikiro anokonzerwa nekukotama mumatangi echimiro che silinda yakatenderera
Ngatitorei tangi rechimiro checylinder rine urefu h rakazadzwa nemvura (fig. 9), ipapo pakureba x pamusoro pematangi maviri kumanikidzwa kwemvura kuri p=γ(h-x). Kana pakureba uku kubva pamacheka maviri akatwasuka akaparadzana ne dx. mhete ikachekwa kubva mutangi uye iyi ikakamurwa nehupamhi hwemudhayamita kuita zvikamu zviviri, mamiriro ekuenzanisa echimwe chezvikamu anopa simba remembrane mumhete Nφ=pa. Kana ukobvu hwetangi panzvimbo iyi t, kuwedzera kureba mumhete kuri εφ=Nφ/Et uye saka kuwedzera kweradius yewotangi (deflection) kuri
Kumucheto kwepasi x=0 saka
Muf. 9
Kana chimwe uye chimwewo kazhinji hazvienderani nemamiriro emipendero, nokuti kukanganisika kwemadziro kunodziviswa nekubatana nepasi petangi. Panguva iyoyo panzvimbo yekubatana pakati pehwaro nemadziro ecylinder panobuda ma transverse forces Qx0 nemamomenti Mx0 (sl. 11), kukura kwawo kunofanira kutsanangurwa zvekuti pamwe chete nemasimba emembrane achangobva kuverengwa mugoko anokonzera kukanganisika uku pamupendero wegoko kunobvumirwa nehwaro.
Muf. 10, 11, 12, zvichitevedzana
Pamuviru. 11 unoratidzwa chinhu chegoko dx*a dφ nemasimba anoita pachiri. Mamiriro ekuenzana kwemasimba munzira yechinyorwa chakamira pagoko anopa
dQx a dφ + Nφ dx dφ = p a dφ dx,
kubva ipapo nekugovera ne dx dφ:
a Q’x + Nφ = p a.
Kubva pamamiriro ekuti momenti yakatenderedza tangent yakatwasuka pane silinda i zero kunowanikwa izvi:
dM/dx = M’x = Qx
Nekubvisa simba retransversal Qx kubva mumazwi maviri aya zvinotevera
a M’’x + Nφ = p a.
Jed. 6
Muequation iyi masimba ekucheka asingazivikanwi aya anogona kuratidzwa kuburikidza nekukotama w. Kune Nφ yava kuwanikwa kuti Nφ=Etw/a, uye moment inoenderana nekukotama kwemeridian w’’, kureva Mx=Kw’’, apo sezvakangoita pamaplate K=Et3/12(1-μ2) kusimba kwegoko, kunogona kuchinja ne x. Kana mazwi aya emasimba epakati akaiswa muequation (6), panowanikwa differential equation yedzidziso yetangi:
Kune tangi rine ukobvu hwemadziro husingachinji, mhinduro ndeiyi:
Poshi.7
uko λ4=3(1-μ2)/a2t2. Kana λh yakakura (ngatiti, kupfuura 3), zviri nyore kushandisa maexponential panzvimbo pemabasa ehyperbolic, saka:
Poshi.8
Ipapo makonstanto A1, B1 anogona kutsanangurwa akazvimirira kubva kune mumwe nemumwe kubva pamiganho yepazasi, uye makonstanto A2, B2 kubva pamiganho yepamusoro, apo kazhinji panowanikwa A2=B2=0. Kubva paequation (8) ne(7) panowanikwa masimba ekucheka, kana kuverenga kukaitwa nenzira yakapesana uye equation (8) ne(7) yaiswa kwese; saka semuenzaniso pa A2=B2=0:
Kana madziro etangi akasungwa zvakasimba mukuplate, pasi petangi riri rakakora zvakakwana kuti rionekwe serakasimba, makonstanti A1, B1 anofanira kutemwa kubva mumamiriro ekuti x=0, w=0 uye w’=0 zvobva zvawanikwa:
Kana pasi petangi iri ndiro inochinjika kana goko, masimba ekuyambuka Qx uye ma-moment Mx parutivi rwedenderedzwa rekunze pakati pechigadziko nerusvingo rwesilinda anofanira kutsanangurwa nenzira dzedzidziso yezvirongwa zvine miganho isina kutsanangurwa, zvichienderana nechido chekuti Mx ne w’ pazvikamu zviviri zvive nekukosha kumwe chete.